Question

Questions Energy levels in the Bohr Hydrogen Atom In this section we will calculate energies for orbits (energy levels) of the Bohr hydrogen atom using the following relationship: - -2.178 x 10- 26) where is the energy (in joules) and is the electron energy level. Allowable values for nare are non-zero, positive integers (1, 2, 3......0). 1) For each value of 2, calculate the energy of the orbit in joules. Please show your work for the calculations for 1 = 1, 2 and Answer the questions that follow. 2. 178 x 10 n = 25,445 x 10" * = 3_2142 X 10-495 1.361 x 10 n=58,712 x 10-20g 2) Which value of n yields the lowest energy? n = what is its energy? 3) Which value of n yields the greatest energy?n=__ what is its energy? 4) Are the energies increasing or decreasing as n becomes larger? Using the energies you calculated above you can calculate the change in energy of an electron (Electron) that drops from one energy (BI) level to another (Er): Electre = E.E: 5) What is Ederron for the transition nr 2 → 1? When an electron drops from one energy level to another a photon with some amount of energy (Episton) can be released. 6) The Law of Conservation of Energy predicts that Ephotos will be the same as 7) What is Eskoro if an electron undergoes a transition from n = 2 → 1? 8) Briefly explain how the magnitude and sign of your answers for question 5 and 7 compare:

Answer 1

1 E = – 2•178 X10 X142) J n-1; E= - 2:178x105 n = 2 ; F = - 5445 x 10193 n = 3; Ez = -2.420 xios J n = 4; EL = -1.361 x 10 9 J in = 5 % E5=:-.8. 712 710 200 n = a.; Ex = 0 2. Lowest energy na 1 E=-2.178x10 3. Greatest n=ce, E = 0 4. Energy, increases as n becomes larger 5. AE = Ez-E, = [-51445x102(-2.178x102] J =(2:178x108 5 445 X10% = 416335 x108 6. Ephatan = Electron=(Ep-E) 7. Ephraton = 1.6335x10'e